Gorka said Trump may call the executive order anything he wants because he's President.
"There are no games," he said on "New Day." "The President can call it whatever he likes because he has the constitutional authority to control whoever comes into the country, Chris. That's his job."
"The Constitution, tradition, precedence and administrative law give him that right," he continued. "If he wants to call it a ban, he's the President, he's the chief officer of this administration, and he has every right to do that."
Upon being pressed by Cuomo about why the administration previously wouldn't say "travel ban," Gorka turned aggressive.
"I'm not going to fall into the trap of us being the spin-meisters when CNN has been one of the greatest purveyors of fake news," he said.
Gorka went on to list several Muslim-majority countries that are not included in the "travel ban," citing them as proof the order was not targeted at one particular religious group.
"The intention is clear that you wanted to target Muslims from those places," Cuomo said. "I see that you're a little slow to want to own that."
"Unfortunately, what you've just spun is classic fake news," Gorka said later in the exchange.
"I don't think it's spin," said Cuomo. "I think that it's a little bit of logic that you're having a tough time dealing with, especially in light of what the President said this morning."
Eventually, Gorka began attacking CNN and Cuomo defended his employer while trying to steer the conversation back toward the tweets and the ban.
"They are not policy," Gorka said of Trump's tweets. "It's not policy. It's social media, Chris. It's social media. You know the difference, right?"
In a string of tweets early Monday morning
, Trump reiterated comments he made in light of the London terror attacks that the travel ban was necessary.
"People, the lawyers and the courts can call it whatever they want, but I am calling it what we need and what it is, a TRAVEL BAN," he tweeted at 6:25 a.m. ET.
"The Justice Dept. should have stayed with the original Travel Ban, not the watered down, politically correct version they submitted to S.C." he added.